It's a paradox of great plays, which are great on account of the profound specificity of their characters and actions, that we try to compress them into neat, autographed theses, hoping that our mark on them will be as lasting as handprints on drying cement rather than sand in the incoming tide. We provide ourselves with generalised conceits - King Lear is "about" fatherhood, Richard III is "about" tyranny, Hedda Gabler is "about" the position of women - which shrivel the beguiling complexities and ambiguities that have drawn us to the plays in the first place. Great plays are great precisely because, to borrow King Lear's words, they show us the "mystery of things" rather than serve as tools for polemic or guides to good living.

That Hedda is a victim (tragic or not) of her gender and social conditions - and of her own self-destructiveness - is unquestionable, and it's quite reasonable to conscript her to the ranks of fighters for the freedom of women while characterising the men in her life as her oppressors; in short, to argue that the play is "about" feminism and patriarchy.

But part of what is so alluring - and daring - about Hedda Gabler is its wit, its unexpected lack of solemnity, its defiance of an audience's expectations, its reluctance to conform to reductive theory. Is there any other dramatic heroine who possesses such an extraordinary confection of characteristics as Hedda? She's feisty, droll and intelligent, yet fatally ignorant of the world and herself. She's snobbish, mean-spirited, small-minded, conservative, cold, bored, vicious. She's sexually eager but terrified of sex; ambitious to be bohemian but frightened of scandal; a desperate romantic fantasist but unable to sustain any loving relationship with anyone, including herself. And yet, in spite of all this, she mesmerises us and compels our pity.

Hedda can't even succeed in dominating the centre of the universe she has created: in the 36 hours of the action of the play she realises that as a mere wife of an academic, she's powerless, imprisoned by her prospective motherhood and indentured to a cruel man as his mistress. Suicide is the only way out, a final, awful, "grand gesture".

"The title of the play," wrote Ibsen in a letter ,"is Hedda Gabler [rather than 'Hedda Tesman' - her husband's name]. I intended to indicate thereby that as a personality she is to be regarded rather as her father's daughter than as her husband's wife." Hedda's father was a general, with the status if not the wealth of an aristocrat and, according to Ibsen's notes, Hedda was born when her father was already an old man and had left the army in slightly discreditable circumstances. Hedda, an orphan (perhaps the mother died in childbirth), is left to vindicate her father's reputation. "She really wants to live the whole life of a man," said Ibsen, but as he said in his notes for A Doll's House: "A woman cannot be herself in modern society. It is an exclusively male society, with laws made by men and with prosecutors and judges who assess feminine conduct from a masculine standpoint."

Which might suggest a schematic creation of a character, but Hedda seems a creation as ambiguous and unpredictable as anyone you might meet in life - and, in the case of a Hedda, avoid. And to her creator she, and indeed everyone in the play, were as real as if they had lived: "Finally, in the last draft, I have reached the limit of my knowledge; I know my characters from close and long acquaintance - they are my intimate friends, who will no longer disappoint me; as I see them now, I shall always see them."

That quality of even-handedly creating characters who seem to exist independently of their maker is not one that I, at least, have often ascribed to Ibsen. It's more, well, a Chekhovian quality, and perhaps it's a confession of ignorance (or banality) that for many years I thought a liking for Chekhov and for Ibsen were incompatible: you declared yourself for one party or the other. "Ibsen is an idiot," said Chekhov, and in my infatuation I was prepared to agree with him. But compare these two statements:

"It was not really my intention to deal in this play with so-called problems. What I principally wanted to do was to depict human beings, human emotions, and human destinies, upon a groundwork of certain of the social conditions and principles of the present day."

"You are right in demanding that an artist approach his work consciously, but you are confusing two concepts: the solution of a problem and the correct formulation of a problem. Only the second is required of the artist."

And then answer the question: which is Chekhov, which Ibsen? The first is Ibsen.

When I was working with the conductor Georg Solti, I asked him what he regretted most: "Not being able to say sorry to Shostakovich for having underrated him and thought of him as a lackey of the state." I've often felt I'd like to apologise to Ibsen for my prejudice. I have a temperamental inclination to Chekhov because of his mordant wit and worldliness, his doctor's eye and his talent for transforming experience of life and love into art. But in fact, at least as far as Hedda Gabler is concerned, Ibsen was doing the same thing. "The essential thing," he said "is ... to draw a clear distinction between what one has merely experienced and what one has spiritually lived through; for only the latter is proper material for creative writing."

It's both pointless and prurient to behave as if there's a linear equation that connects life (particularly love-life) and art, but in the case of Hedda Gabler there's no question that events in Ibsen's life were a catalyst to his creative process, a crystal of lived experience around which the play coalesced.

In the summer of 1889, when he was 61, Ibsen was on holiday in a south Tyrolean village. He met an 18-year-old Viennese girl called Emilie Bardach and fell in love. He had dedicated himself to his art like a monk, for "the power and the glory", and he had renounced spontaneous joy and sexual fulfilment. Emilie became the "May sun of a September life". She asked him to live with her; he at first agreed but, crippled by guilt and fear of scandal (and perhaps impotence as well), put an end to the relationship.

Emilie, like Hedda, was a beautiful, intelligent, spoilt, bored upper-class girl with "a tired look in her mysterious eyes", who wanted to have power and was thrilled at the possibility of snaring someone else's husband. The village in which they met in the Tyrol - Gossensass - was mentioned specifically in an earlier draft of the play when Hedda and Loevborg are looking at the honeymoon photographs in the second act, and fragments of dialogue in Ibsen's notes from the play appear to be derived directly from his conversations with Emilie.

But, if Emilie was the inspiration for the character of Hedda, Ibsen himself - consciously or not - contributed many of her characteristics. With his fear of scandal and ridicule, his apparent repulsion with the reality of sex, his yearning for an emotional freedom, Ibsen might have said of Hedda, as Flaubert did of Madame Bovary: "Hedda, c'est moi."

There were two entirely unconnected events which occurred last year that drew my attention to the play. I was sitting in a dentist's waiting room reading an interview in Hello! magazine with a rich young woman who was celebrated for being celebrated. She craved attention and yet had no talent for anything but self-advertisement and was quoted, without irony (never the strong suit of Hello!), as saying: "I'm afraid I have a great talent for boredom."

Mmmm, I thought, Hedda Gabler lives. The same evening I went to a fine production of Eugene O'Neill's Mourning Becomes Electra and saw an actress, Eve Best, who seemed born to play Hedda. I took the synchronicity as a sign that I should do the play and got myself commissioned by Robert Fox and by Michael Attenborough at the Almeida Theatre to do a new translation.

The best way of understanding a play is to write it - even if that means merely typing a script yourself or copying it out in longhand. It obliges you to question the meaning of every word, speech, gesture and stage direction. Arthur Miller once said to me: "You know what I used to do years ago? I would take any of Shakespeare's plays and simply copy them. Pretending that I was him, you see. You know, it's a marvellous exercise. Just copy the speeches, and you gradually realise the concision, the packing together of experience, which is hard to do just with your ear, but if you have to work it with a pen or a piece of paper, you see that stuff coming together in that intense inner connection of sound and meaning."

Which is what I've tried to do in this version of Ibsen's great play. It can't properly be called a "translation" because I speak not a word of Norwegian. I worked from a literal version by Karin and Ann Bamborough, and I tried to animate the language in a way that felt as true as possible to what I understood from them to be the author's intentions - even to the point of trying to capture cadences that I could at least infer from the Norwegian original. But even literal translations make choices and the choices we make are made according to taste, to the times we live in and how we view the world. All choices are choices of meaning, of intention. What I have written is a "version" or "adaptation" or "interpretation" of Ibsen's play, but I hope that it comes close to what Ibsen intended while seeming spontaneous to an audience of today.

· Hedda Gabler opens at the Almeida, London N1 (020-7359 4404), on Thursday